'The polymerase chain reaction (PCR) is a biomedical technology in molecular biology used to amplify a single copy or a few copies of a piece of DNA across several orders of magnitude, generating thousands to millions of copies of a particular DNA sequence' (wikipedia PCR page).

Each cycle amplifies the original DNA sample set of molecules by a factor of 2 (as in natural gene duplication). After 30 cycles then, the number of molecules will be amplified by a factor of 2^30.

We are given that we start with 1ng (microgram = 10^-6 grams) of (assumed whole) human DNA molecules. We could calculate the number of molecules present in that sample using the fact that 1 base pair (=2 nucleoside phosphates) weighs 660 Da (Dalton) and that there are approximately 3 x 10^9 base pairs in the human genome, and that 1 Dalton = 1.66 x 10^-24 grams. However, all we in fact need to know is the amplication factor, 2^30 and the length of the DNA segment of interest relative to the length of a DNA molecule as a whole.

The DNA segment of interest is 330 base pairs, and the entire length is approximately 3 x 10^9 base pairs long. Therefore only a fraction

330/(3x 10^9) = 110 x 10^-9 = 1.10 x 10^-7 ng

of the original DNA molecule sample is amplified up by the primer (which we hope targets that segment of DNA only).

The resulting weight of the PCR product then will be 2^30 times this original weight of the target segment (where we consider the replication of the segment of interest only and not the imprint of the primer on the amplicons of the segment).

The resulting weight is then

1.10 x 10^-7 x 2^30 = 118.1116 = 118 ng to 3sf

(If the imprint of the primer on the amplicons is approximately the same weight as the DNA segment of interest in the amplicons, the PCR product's actual weight, including the part pertaining to the DNA segment we're interested in and the part caused by the chemical reaction with the primer, would be roughly double this)